Lemma 2.4 (Composition of zCDP [1]}) 

Let \(\mathcal {M}: \mathcal {X}^n \rightarrow \mathcal {Y}\)  and
\(\mathcal {M}^{\prime }: \mathcal {X}^n \rightarrow \mathcal {Z}\)  such that
\(\mathcal {M}\)  satisfies \(\rho \) -zCDP and \(\mathcal {M}^{\prime }\)  satisfies \(\rho ^{\prime }\) -zCDP.
Define \(\mathcal {M}^{\prime \prime } : \mathcal {X}^n \rightarrow \mathcal {Y} \times \mathcal {Z}\)  by
\(\mathcal {M}^{\prime \prime }(x) = \left( \mathcal {M}(x), \mathcal {M}^{\prime }(x) \right)\) .
Then \(\mathcal {M}^{\prime \prime }\)  satisfies \((\rho + \rho ^{\prime })\) -zCDP.

